Hallie Can Use The Equation P = 4 L + 4 W + 4 H P=4l+4w+4h P = 4 L + 4 W + 4 H To Determine The Sum Of The Lengths Of The Edges Of A Rectangular Prism. She Begins To Solve The Equation For H H H But Runs Out Of Time. Her Partial Work Is Shown Below:1. P = 4 L + 4 W + 4 H P=4l+4w+4h P = 4 L + 4 W + 4 H

Introduction

In mathematics, solving equations is a crucial skill that helps us understand and analyze various problems. Hallie, a student, is working on an equation to determine the sum of the lengths of the edges of a rectangular prism. The equation is $p=4l+4w+4h$, where $p$ represents the sum of the lengths of the edges, $l$ is the length, $w$ is the width, and $h$ is the height of the prism. In this article, we will guide Hallie and other students on how to solve for height in a rectangular prism using the given equation.

Understanding the Equation

The equation $p=4l+4w+4h$ represents the sum of the lengths of the edges of a rectangular prism. To solve for height, we need to isolate the variable $h$ on one side of the equation. The equation can be rewritten as $p-4l-4w=4h$. This equation shows that the sum of the lengths of the edges minus the sum of the lengths of the length and width is equal to four times the height.

Step 1: Subtract 4l and 4w from Both Sides

To isolate the variable $h$, we need to get rid of the terms $4l$ and $4w$ on the left-hand side of the equation. We can do this by subtracting $4l$ and $4w$ from both sides of the equation. This gives us:

$$p-4l-4w=4h$$

Subtracting $4l$ and $4w$ from both sides gives us:

$$p-4l-4w-4l-4w=4h-4l-4w$$

Simplifying the left-hand side, we get:

$$p-8l-8w=4h-4l-4w$$

Step 2: Add 4l and 4w to Both Sides

To isolate the variable $h$, we need to get rid of the terms $-4l$ and $-4w$ on the right-hand side of the equation. We can do this by adding $4l$ and $4w$ to both sides of the equation. This gives us:

$$p-8l-8w+4l+4w=4h-4l-4w+4l+4w$$

Simplifying the left-hand side, we get:

$$p-4l-4w=4h$$

Step 3: Divide Both Sides by 4

To isolate the variable $h$, we need to get rid of the coefficient $4$ on the right-hand side of the equation. We can do this by dividing both sides of the equation by $4$. This gives us:

$$\frac{p-4l-4w}{4}=\frac{4h}{4}$$

Simplifying the right-hand side, we get:

$$\frac{p-4l-4w}{4}=h$$

Conclusion

In this article, we have guided Hallie and other students on how to solve for height in a rectangular prism using the equation $p=4l+4w+4h$. We have shown that by subtracting $4l$ and $4w$ from both sides, adding $4l$ and $4w$ to both sides, and dividing both sides by $4$, we can isolate the variable $h$ and solve for height. This skill is essential in mathematics and can be applied to various problems involving equations and variables.

Real-World Applications

Solving for height in a rectangular prism has many real-world applications. For example, in architecture, engineers need to calculate the height of buildings and other structures to ensure that they are safe and stable. In manufacturing, companies need to calculate the height of products to ensure that they fit properly in packaging and shipping. In science, researchers need to calculate the height of objects to understand their properties and behavior.

Tips and Tricks

When solving for height in a rectangular prism, it is essential to follow the order of operations (PEMDAS) and to simplify the equation as much as possible. It is also essential to check the units of measurement to ensure that they are consistent. Additionally, it is helpful to use visual aids such as diagrams and graphs to understand the problem and to check the solution.

Common Mistakes

When solving for height in a rectangular prism, there are several common mistakes that students make. One common mistake is to forget to subtract $4l$ and $4w$ from both sides of the equation. Another common mistake is to forget to add $4l$ and $4w$ to both sides of the equation. Additionally, students may forget to divide both sides of the equation by $4$ to isolate the variable $h$.

Conclusion

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Q: What is the equation for the sum of the lengths of the edges of a rectangular prism?

A: The equation for the sum of the lengths of the edges of a rectangular prism is $p=4l+4w+4h$, where $p$ represents the sum of the lengths of the edges, $l$ is the length, $w$ is the width, and $h$ is the height of the prism.

Q: How do I solve for height in a rectangular prism using the equation $p=4l+4w+4h$?

A: To solve for height in a rectangular prism using the equation $p=4l+4w+4h$, you need to follow these steps:

1. Subtract $4l$ and $4w$ from both sides of the equation.
2. Add $4l$ and $4w$ to both sides of the equation.
3. Divide both sides of the equation by $4$.

Q: What is the formula for solving for height in a rectangular prism?

A: The formula for solving for height in a rectangular prism is $h=\frac{p-4l-4w}{4}$.

Q: What are some real-world applications of solving for height in a rectangular prism?

A: Some real-world applications of solving for height in a rectangular prism include:

• Architecture: Engineers need to calculate the height of buildings and other structures to ensure that they are safe and stable.
• Manufacturing: Companies need to calculate the height of products to ensure that they fit properly in packaging and shipping.
• Science: Researchers need to calculate the height of objects to understand their properties and behavior.

Q: What are some common mistakes to avoid when solving for height in a rectangular prism?

A: Some common mistakes to avoid when solving for height in a rectangular prism include:

• Forgetting to subtract $4l$ and $4w$ from both sides of the equation.
• Forgetting to add $4l$ and $4w$ to both sides of the equation.
• Forgetting to divide both sides of the equation by $4$.

Q: How can I check my solution for height in a rectangular prism?

A: To check your solution for height in a rectangular prism, you can use visual aids such as diagrams and graphs to understand the problem and to check the solution. You can also plug in values for $l$, $w$, and $p$ to see if the solution is correct.

Q: What is the importance of solving for height in a rectangular prism?

A: Solving for height in a rectangular prism is an essential skill that has many real-world applications. It is used in various fields such as architecture, manufacturing, and science. By mastering this skill, you can apply it to various problems involving equations and variables.

Q: Can I use this formula to solve for height in other shapes?

A: No, this formula is specifically designed for rectangular prisms. If you need to solve for height in other shapes, you will need to use a different formula.

Q: How can I practice solving for height in a rectangular prism?

A: You can practice solving for height in a rectangular prism by using online resources, such as worksheets and practice problems. You can also try solving problems on your own using the formula and checking your solutions using visual aids and plugging in values.

Q: What are some additional resources for learning about solving for height in a rectangular prism?

A: Some additional resources for learning about solving for height in a rectangular prism include:

• Online tutorials and videos
• Textbooks and workbooks
• Online communities and forums
• Math apps and software